you are deaIt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black.
There are 26 black cards in a standard deck of 52 playing cards.
When the first card is drawn, there are a total of 52 cards, 26 of which are black. Thus, the probability of drawing a black card as the first card is 26/52 or 1/2.
After the first card is drawn, there are now 51 cards remaining, and 25 of them are black. Therefore, the probability of drawing a black card as the second card is 25/51.
To find the probability that both cards are black, we multiply the probabilities of each event occurring, since these events are independent (the outcome of the first card does not affect the outcome of the second card).
Probability of both cards being black = (1/2) * (25/51) = 25/102
Therefore, the probability that both cards drawn successively (without replacement) from a shuffled deck of 52 playing cards are black is 25/102.